Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Filling Disks of Hayman Type of Meromorphic Functions Tue, 31 May 2016 11:24:34 +0000 We obtain the existence of the filling disks with respect to Hayman directions. We prove that, under the condition , there exists a sequence of filling disks of Hayman type, and these filling disks can determine a Hayman direction. Every meromorphic function of positive and finite order has a sequence of filling disks of Hayman type, which can also determine a Hayman direction of order . Nan Wu and Zuxing Xuan Copyright © 2016 Nan Wu and Zuxing Xuan. All rights reserved. On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials Mon, 30 May 2016 12:29:53 +0000 We provide the proof of a practical pointwise characterization of the set defined by the closure set of the real projections of the zeros of an exponential polynomial with real frequencies linearly independent over the rationals. As a consequence, we give a complete description of the set and prove its invariance with respect to the moduli of the , which allows us to determine exactly the gaps of and the extremes of the critical interval of by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance. J. M. Sepulcre Copyright © 2016 J. M. Sepulcre. All rights reserved. Hadamard Multipliers and Abel Dual of Hardy Spaces Mon, 30 May 2016 12:29:11 +0000 The paper is devoted to the study of Hadamard multipliers of functions from the abstract Hardy classes generated by rearrangement invariant spaces. In particular the relation between the existence of such multiplier and the boundedness of the appropriate convolution operator on spaces of measurable functions is presented. As an application, the description of Hadamard multipliers into is given and the Abel type theorem for mentioned Hardy spaces is proved. Paweł Mleczko Copyright © 2016 Paweł Mleczko. All rights reserved. Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions Mon, 30 May 2016 09:41:38 +0000 Using simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman integration theories and quantum mechanics. We then establish various integral transforms over continuous paths with change of scales for the generalized analytic conditional Wiener integrals. In these evaluation formulas and integral transforms we use multivariate normal distributions so that the orthonormalization process of projection vectors which are needed to establish the conditional Wiener integrals can be removed in the existing change of scale transforms. Consequently the transforms in the present paper can be expressed in terms of the generalized cylinder function itself. Dong Hyun Cho Copyright © 2016 Dong Hyun Cho. All rights reserved. Uniform Attractors for Nonclassical Diffusion Equations with Memory Mon, 30 May 2016 07:55:13 +0000 We introduce a new method (or technique), asymptotic contractive method, to verify uniform asymptotic compactness of a family of processes. After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearity satisfies the polynomial growth of arbitrary order and the time-dependent forcing term is only translation-bounded in . Yongqin Xie, Yanan Li, and Ye Zeng Copyright © 2016 Yongqin Xie et al. All rights reserved. A New Approach to Fuzzy Metric Spaces and Their Similarity-Based Construction Thu, 26 May 2016 05:56:58 +0000 We introduce a space of functions which can be interpreted as a similarity-based approach to fuzzy metric spaces. The triangle inequality we propose is defined by means of a fuzzy ordering. We compare the introduced space with fuzzy metric spaces in the sense of Seikkala and Kaleva. Finally we complete the work discovering the corresponding classical as well as fuzzy topologies. Gültekin Soylu and Mutlu Güloğlu Copyright © 2016 Gültekin Soylu and Mutlu Güloğlu. All rights reserved. Ulam-Hyers Stability for MKC Mappings via Fixed Point Theory Wed, 25 May 2016 13:30:11 +0000 We consider some extension of MKC mappings in the framework of complete dislocated metric spaces. Besides the theoretical results, we also consider some illustrative examples. Further, we state and prove that our main results improved the related results in the frame of generalized Ulam-Hyers stability theory. Anisa Mukhtar Hassan, Erdal Karapınar, and Hamed H. Alsulami Copyright © 2016 Anisa Mukhtar Hassan et al. All rights reserved. Commutative -Algebras of Toeplitz Operators via the Moment Map on the Polydisk Sun, 22 May 2016 14:01:42 +0000 We found that in the polydisk there exist different classes of commutative -algebras generated by Toeplitz operators whose symbols are invariant under the action of maximal Abelian subgroups of biholomorphisms. On the other hand, using the moment map associated with each (not necessary maximal) Abelian subgroup of biholomorphism we introduced a family of symbols given by the moment map such that the -algebra generated by Toeplitz operators with this kind of symbol is commutative. Thus we relate to each Abelian subgroup of biholomorphisms a commutative -algebra of Toeplitz operators. Mauricio Hernández-Marroquin, Armando Sánchez-Nungaray, and Luis Alfredo Dupont-García Copyright © 2016 Mauricio Hernández-Marroquin et al. All rights reserved. On Subordinations for Certain Multivalent Analytic Functions in the Right-Half Plane Tue, 17 May 2016 12:05:09 +0000 The object of the present paper is to investigate some properties of multivalent analytic functions associated with the lemniscate of Bernoulli. Yi-Hui Xu and Jin-Lin Liu Copyright © 2016 Yi-Hui Xu and Jin-Lin Liu. All rights reserved. Liouville Theorem for Some Elliptic Equations with Weights and Finite Morse Indices Thu, 12 May 2016 13:59:58 +0000 We establish the nonexistence of solution for the following nonlinear elliptic problem with weights: in , where is a positive parameter. Suppose that , for or , for ; we will show that this equation does not possess nontrivial bounded solution with finite Morse index. Qiongli Wu, Liangcai Gan, and Qingfeng Fan Copyright © 2016 Qiongli Wu et al. All rights reserved. Classes of -Convergent Double Sequences over -Normed Spaces Mon, 09 May 2016 13:34:49 +0000 I introduce some new classes of -convergent double sequences defined by a sequence of moduli over -normed space. Study of their algebraic and topological properties and some inclusion relations has also been done. Nazneen Khan Copyright © 2016 Nazneen Khan. All rights reserved. Trace Operators on Wiener Amalgam Spaces Sun, 08 May 2016 12:52:47 +0000 The paper deals with trace operators of Wiener amalgam spaces using frequency uniform decomposition operators and maximal inequalities, obtaining sharp results. Additionally, we provide the embedding between standard and anisotropic Wiener amalgam spaces. Jayson Cunanan and Yohei Tsutsui Copyright © 2016 Jayson Cunanan and Yohei Tsutsui. All rights reserved. Weighted Estimates of a Class of Integral Operators with Three Parameters Sat, 30 Apr 2016 10:51:00 +0000 We characterize the validity of a Hardy-type inequality with a kernel and three parameters under some conditions on three weight functions , , and . Ryskul Oinarov and Aigerim Kalybay Copyright © 2016 Ryskul Oinarov and Aigerim Kalybay. All rights reserved. Input-to-State Stability of Linear Stochastic Functional Differential Equations Thu, 28 Apr 2016 13:59:08 +0000 The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we call input-to-state stability with respect to these spaces. Input-to-state stability and hence the desired asymptotic properties can be effectively verified by means of a special regularization, also known as “the -method” in the literature. How this framework provides verifiable conditions of different kinds of stochastic stability is shown. Ramazan Kadiev and Arcady Ponosov Copyright © 2016 Ramazan Kadiev and Arcady Ponosov. All rights reserved. Some Extensions of Fixed Point Results over Quasi--Spaces Thu, 28 Apr 2016 12:37:03 +0000 We introduce the notion of quasi--metric space. After defining the basic topological properties of quasi--metric space, we investigate fixed point of certain mapping in the frame of complete quasi--metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi--metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature. Maha Noorwali, Hamed H. Alsulami, and Erdal Karapınar Copyright © 2016 Maha Noorwali et al. All rights reserved. Periodic Orbits of Radially Symmetric Keplerian-Like Systems with a Singularity Mon, 18 Apr 2016 14:05:27 +0000 We study planar radially symmetric Keplerian-like systems with repulsive singularities near the origin and with some semilinear growth near infinity. By the use of topological degree theory, we prove the existence of two distinct families of periodic orbits; one rotates around the origin with small angular momentum, and the other one rotates around the origin with both large angular momentum and large amplitude. Shengjun Li and Yuming Zhu Copyright © 2016 Shengjun Li and Yuming Zhu. All rights reserved. A Characterization of Symmetric Stable Distributions Sun, 17 Apr 2016 06:57:40 +0000 Characterization problems in probability are studied here. Using the characteristic function of an additive convolution we generalize some known characterizations of the normal distribution to stable distributions. More precisely, if a distribution of a linear form depends only on the sum of powers of the certain parameters, then we obtain symmetric stable distributions. Wiktor Ejsmont Copyright © 2016 Wiktor Ejsmont. All rights reserved. Solutions for Impulsive Fractional Differential Equations via Variational Methods Thu, 14 Apr 2016 16:01:34 +0000 We investigate the boundary value problems of impulsive fractional order differential equations. First, we obtain the existence of at least one solution by the minimization result of Mawhin and Willem. Then by the variational methods and a very recent critical points theorem of Bonanno and Marano, the existence results of at least triple solutions are established. At last, two examples are offered to demonstrate the application of our main results. Peiluan Li, Hui Wang, and Zheqing Li Copyright © 2016 Peiluan Li et al. All rights reserved. On the Initial Value Problem of Stochastic Evolution Equations in Hilbert Spaces Tue, 12 Apr 2016 09:01:15 +0000 The present paper studies the initial value problem of stochastic evolution equations with compact semigroup in real separable Hilbert spaces. The existence of saturated mild solution and global mild solution is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions. The results obtained in this paper improve and extend some related conclusions on this topic. An example is also given to illustrate that our results are valuable. Xuping Zhang, Yongxiang Li, and Pengyu Chen Copyright © 2016 Xuping Zhang et al. All rights reserved. Estimates for Parameter Littlewood-Paley Functions on Nonhomogeneous Metric Measure Spaces Mon, 11 Apr 2016 11:14:12 +0000 Let be a metric measure space which satisfies the geometrically doubling measure and the upper doubling measure conditions. In this paper, the authors prove that, under the assumption that the kernel of satisfies a certain Hörmander-type condition, is bounded from Lebesgue spaces to Lebesgue spaces for and is bounded from into . As a corollary, is bounded on for . In addition, the authors also obtain that is bounded from the atomic Hardy space into the Lebesgue space . Guanghui Lu and Shuangping Tao Copyright © 2016 Guanghui Lu and Shuangping Tao. All rights reserved. A Generalization of Uniformly Extremely Convex Banach Spaces Sun, 10 Apr 2016 13:14:23 +0000 We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes of -uniformly rotund spaces and -strongly convex spaces or classes of fully -convex spaces and -strongly convex spaces and has no inclusive relation with the class of locally -uniformly convex spaces. We obtain in addition some characterizations and properties of this new class of Banach spaces. In particular, our results contain the main results of Wulede and Ha. Suyalatu Wulede, Wurichaihu Bai, and Wurina Bao Copyright © 2016 Suyalatu Wulede et al. All rights reserved. Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces Wed, 06 Apr 2016 13:44:44 +0000 Let be a generalized Calderón-Zygmund operator or (the identity operator), let and be the linear operators, and let . Denote the Toeplitz type operator by , where and is the fractional integral operator. In this paper, we investigate the boundedness of the operator on weighted Morrey space when belongs to the weighted BMO spaces. Bijun Ren and Enbin Zhang Copyright © 2016 Bijun Ren and Enbin Zhang. All rights reserved. A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Type Functional Equation Wed, 06 Apr 2016 08:18:21 +0000 By applying a fixed point approach, we investigate the stability problems for an AQCQ functional equation of the form Yang-Hi Lee and Soon-Mo Jung Copyright © 2016 Yang-Hi Lee and Soon-Mo Jung. All rights reserved. A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions Wed, 06 Apr 2016 08:12:17 +0000 Existence and uniqueness results of positive solutions to nonlinear boundary value problems for Caputo-Hadamard fractional differential equations by using some fixed point theorems are presented. The related Green’s function for the boundary value problem is given, and some useful properties of Green’s function are obtained. Example is presented to illustrate the main results. Wafa Shammakh Copyright © 2016 Wafa Shammakh. All rights reserved. On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping Tue, 05 Apr 2016 09:37:05 +0000 The concept of -frame which is a generalization of the frame in Hilbert spaces generated by the bilinear mapping is considered. -frame operator is defined; analogues of some well-known results of frame theory are obtained in Hilbert spaces. Conditions for the existence of -frame in Hilbert spaces are obtained; the relationship between the definite bounded surjective operator and -frame is also studied. The concept of -orthonormal -basis is introduced. Migdad Ismailov, Fatima Guliyeva, and Yusif Nasibov Copyright © 2016 Migdad Ismailov et al. All rights reserved. Weighted Estimates for Toeplitz Operators Related to Pseudodifferential Operators Sun, 03 Apr 2016 14:25:59 +0000 The authors establish the weighted estimates for a class of pseudodifferential operators for both cases and , where the weight class is bigger than the classical Muckenhoupt’s weight class. Moreover, the weighted estimates for the Toeplitz operators related to pseudodifferential operators are also obtained. As their special cases, the corresponding results for the commutators of pseudodifferential operators can be deduced. Yan Lin, Zongguang Liu, Chengdan Xu, and Zichu Ren Copyright © 2016 Yan Lin et al. All rights reserved. On the Superstability of Lobačevskiǐ’s Functional Equations with Involution Sun, 03 Apr 2016 13:41:22 +0000 Let be a uniquely -divisible commutative group and let and be an involution. In this paper, generalizing the superstability of Lobačevskiǐ’s functional equation, we consider or for all , where . As a direct consequence, we find a weaker condition for the functions satisfying the Lobačevskiǐ functional inequality to be unbounded, which refines the result of Găvrută and shows the behaviors of bounded functions satisfying the inequality. We also give various examples with explicit involutions on Euclidean space. Jaeyoung Chung, Bogeun Lee, and Misuk Ha Copyright © 2016 Jaeyoung Chung et al. All rights reserved. Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation Sun, 03 Apr 2016 09:51:18 +0000 This paper deals with the second-order nonlinear neutral delay difference equation , . Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field. Zeqing Liu, Xin Li, Shin Min Kang, and Young Chel Kwun Copyright © 2016 Zeqing Liu et al. All rights reserved. Discussion on Some Recent Order-Theoretic Metrical Coincidence Theorems Involving Nonlinear Contractions Wed, 30 Mar 2016 08:53:28 +0000 We prove some coincidence theorems involving a pair of self-mappings and defined on an ordered metric space wherein is -increasing -contractive mapping. In our results, neither the whole space nor the range subspaces ( or ) are required to be complete. Instead, we use the completeness of a subspace of satisfying suitable conditions. Aftab Alam, Qamrul Haq Khan, and Mohammad Imdad Copyright © 2016 Aftab Alam et al. All rights reserved. Fractional Calculus of Analytic Functions Concerned with Möbius Transformations Tue, 22 Mar 2016 16:00:56 +0000 Let be the class of functions in the open unit disk with and . Also, let be a Möbius transformation in for some . Applying the Möbius transformations, we consider some properties of fractional calculus (fractional derivatives and fractional integrals) of . Also, some interesting examples for fractional calculus are given. Nicoleta Breaz, Daniel Breaz, and Shigeyoshi Owa Copyright © 2016 Nicoleta Breaz et al. All rights reserved.